COMP 4804: Design and Analysis
of Algorithms II
Term: Fall 2017 Class Hours: Mondays and
Wednesdays 1005-1125 in CBY 3400
Office Hours: Tuesday from 09:00 to 11:30 or walk in
when the door is open, or send an e-mail. (It is likely that some
Tuesdays the office hour may be more busy with COMP 3801 students. I
have given them slot from 10-11:30. It is advisable to please come
early around 9AM on Tuesdays (Thanks)).
Teaching Assistant: Darryl Hill
Office Hours:
Mondays and Wednesdays from 13:00-14:00 in HP 4125.
Course Prerequisite: COMP 3804 (Preferably with
high grades)
What is it about
(a.k.a. Calender description):
A second course on the design and
analysis of algorithms. Topics include: advanced recurrence
relations, algebraic complexity, advanced graph algorithms,
amortized analysis, algorithms for NP-complete problems,
randomized algorithms.
Focus will be on the last three topics, likely in the reverse order.
Course will require proofs - most often including probability. You
should be familiar with basic graph algorithms (dfs, bfs, MST,
SSSP), basic data structures (dynamic trees, heaps, order
statistics), analysis of algorithms (recurrences,
substitution), some ideas on how to prove the correctness of
an algorithm (induction, contradiction, ..), basic probability -
conditional probability, expected value, birthday problem, indicator
r.v., etc. For your reference, final exams for COMP 2804 and COMP
3804 are provided as Assignment 0 for a quick refresher.
Topics that will likely be covered include: Approximation algorithms
for: vertex cover (including FPTs and rounding method for
weighted vertex cover), TSP, load balancing in identical machines,
set cover, k-center clustering, subset sum, knapsack.
Probabilistic inequalities including Markov, Chebyshev, and
Chernoff. Randomized algorithms for:
verifying polynomial identity and matrix multiplication, Minimum
Spanning Trees, Minimum Cut, Binary Search Trees, Occupancy Problems
(Balls & Bins), Closest Pair, Binary Space Partition, Set
Balancing and Routing. Data structures favoring amortized analysis.
Course Text Book:
Main: Kleinberg/Tardos's Algorithm Design (Addison-Wesley 2005),
Secondary: Cormen et al. (CLRS) Algorithms (MIT Press 2009),
and Dasgupta, Papadimitriou, Vazirani's Algorithms
(McGraw 2007).
I have some
ClassNotes for another course, and may land up touching
some material from there.
Likely some Research Papers that will be outlined in the class -
most of them should be available from our Library.
Course References:
(Leighton) F.T. Leighton, "Introduction to parallel
architectures and algorithms", Morgan Kaufman.
(Knuth) D.E. Knuth, "The art of computer programming", Vol.
1,2,3 Addison-Wesley.
(Kozen) Dexter Kozen, "The design and analysis of
Algorithms", Springer 1992
(Tarjan) Robert Tarjan, " Data structures and algorithms",
SIAM Press.
(Motwani/Raghavan) R. Motwani and P. Raghavan, "Randomized
Algorithms".
(CLRS) Introduction to Algorithms, Cormen Leiserson Rivest and
Stein (3rd Edition)
(Dasgupta, Papadimitriou, Vazirani. "Algorithms", McGraw.
(MU) Mitzenmacher and Upfal, "Probability and Computing" Cambridge
2005
(WS) Williamson and Shymos, The design of
approximation algorithms, 2010
Some Journal/Conference Articles.
Course evaluation:
- 6 Assignments: 30%
Note: All Assignments are due at the start of the class.
Solutions will be provided in the class.
- Quizzes: 10%
During the class - expect about one
quiz/week and they will be without any advance notice as they
depend on the coverage of the topics.
- Mid-Term: 20%
In Class on Nov 01.
- Final Exam: 40%
Date and Location are announced by the
Examination Services
(Note: To pass the course you need to obtain at least 50% Marks
in the Final Exam AND at least 50% Marks overall.)
Plan for Fall 2017
Sept 06: Course Logistics. What will we see in this course?
Approximation Algorithms for (Weighted) Vertex Cover in a Graph.
Sept 11: Approximation algorithms for Vertex Cover,
Weighted Vertex Cover, [Look into Wikipedia page on Vertex Cover
and references therein. Chapter 11 of
the Textbook.
Sept 13: FPT for Vertex Cover [1], A Load
Balancing Problem [See 1
2]
+ Chapter 11 of the Textbook.
Sept 18: TSP [See 1] (Q1: 3/2
approximation for greedy load balancing after sorting.)
Sept 20: A1 Due,
Short discussion on solutions for questions in the Assignment,
3/2 approximation to TSP, Approximation algorithm for Set Cover
(and its connection to the Hospital Optimization problem)
Sept 25: Approximating Set Cover
(1)
and Exact Subset Sum.
Sept 27: Approximating Subset
Sum (Section 35.5 of CLRS) + Clustering Problem (Q2: Why is the value
returned by the exact subset sum is optimal.)
Oct 02: Clustering + Largest independent set
of squares
Oct 04: A2 Due, Approximating Knapsack
(Section
3.1 of WS book)
Oct 09: Thanksgiving
Oct 11:
Finishing the FPTAS for knapsack + Randomized Algorithms - an Intro (Consult
Chapter on Probability for CS in
ClassNotes)
Oct 16:
Randomized algorithms for Verification (Polynomial,
Matrix [1]
[2],
Strings)
Oct 18: Min-Cut (See
1
2 )
and Max-SAT [1
(Skip De-randomization) 2][Q4:
Prove linearity of expectation.]
Oct 30: A3 Due + Review for Mid-Term
Nov 01: Mid-Term
Nov 06: Weighted
MAXSAT (Algorithm I: Simple Random Assignment, Algorithm II:
ILP->LP relaxation-> Randomized Rounding)
Nov 08: Weighted MAXSAT (Analysis + New
algorithm that combines Algorithm I & II ), Randomized Load
Balancing
Nov 13: Chernoff Bounds
(Consult my notes) with some simple examples. Randomized Routing.
Nov 15: A4 Due. Hypercubes and 2-phase randomized
routing algorithm in Hypercubes [1
2]
Nov 20: Finishing
Routing + Randomized MST (Consult my course notes).
Nov 22: Randomized
MST [KKT
Paper]
+ Some
Applications of Chernoff Bounds
Nov 27: A5 Due Finishing the proof of Lemma on the
expected number of light edges [Timothy
Chan Paper]
Nov 29: Closest Pair Problem [1].
Binary Space Partition
Dec 04: BSP Partition [1
2].
Finding Smallest Enclosing Disc for a set of points in plane [1
2].
Dec 06: Smallest Enclosing Discs contd. Applications of
Chernoff Bounds.
Dec 08: A6 Due Review
for Final. Solutions to some problems from Assignments 6 and 4.
Announcements
- All the Carleton's standard rules on Equity, Students
with special needs, Plagiarism, Academic Integrity etc. hold
for this course. All these matters will be handled by
appropriate authorities. You should look into the relevant
university publications, and if you have questions regarding
any of this, you can ask the School of Computer Sciences
Administrative Staff.
- It will be your responsibility to adhere to all
deadlines. Missing a deadline amounts to receiving a Mark of
`zer0' on that component.
- All assignments are due at the beginning of the class.
The solutions of the assignment will likely be provided (in
class on the board) on the due date.
- Assignment 1 is posted on Sept 12. Due in Sept 20th
class.
- Assignment 2 is posted. Due in Oct 4th class.
- Assignment 3 is posted.
- Midterm syllabus includes all the material covered in the
classes as well as in the assignments.
- I am away Oct 30- Nov3. Darryl will take Monday Oct 30th
class and will go over the solutions of Assignment 3 and
possibly a few more problems. He will also conduct the midterm
on Nov 1st.